1. Limits and Continuity

Which of the following statements are correct? Choose all that apply.

a. lim x→1 1/ (x−1)^2 does not exist

b. lim x→1 1/ (x−1)^2=∞

c. lim x→1 1/(x−1)^2=−∞

Determine the following limits.

a. lim x→2^+ 1 x − 2

Determine the following limits.

b. lim x→3^− 2/(x − 3)^3

Determine the following limits.

a. lim x→4^+ x − 5 / (x − 4)^2

Determine the following limits.

b. lim x→4^− x − 5 / (x − 4)^2

Determine the following limits.

c. lim x→4 x − 5 / (x − 4)^2

Determine the following limits.

a. lim x→1^+ x / |x − 1|

Determine the following limits.

c. lim x→1 x / |x − 1|

Determine the following limits.

a. lim z→3^+ (z − 1)(z − 2) / (z − 3)

The graph of ℎ in the figure has vertical asymptotes at x=−2 and x=3. Analyze the following limits. <IMAGE>

lim x→−2 h(x)

Determine the following limits.

a. lim x→−2^+ (x − 4) / x(x + 2)

Determine the following limits.

b. lim x→−2^− (x − 4) / x(x + 2)

Determine the following limits.

c. lim x→−2 (x − 4) / x(x + 2)

Determine the following limits.

a. lim x→2^+ x^2 − 4x + 3 / (x − 2)^2

Determine the following limits.

b. lim t→−2^− t^3 − 5t^2 + 6t / t^4 − 4t^2